There’s no official Tezos Academy body that can set prescriptive rules for how words are to be used. No one can stop you from referring to the Tezos network as the Intertez if that’s where your heart truly is. That being said, I would like to suggest adherence to the following nomenclature as it seems conducive to minimizing confusion .
Used somewhat interchangeably, either as a noun or an adjective to designate:
A open-source project and software (as in, “contributing to the Tezos codebase”)
A peer to peer network of nodes maintaining a blockchain (as in “a Tezos node”)
The specific Tezos chain with the most economic relevance (as in “the Tezos chain”). Typically, this would be today the chain whose millionth block had hash BKtC4QCWoF73kxLj773vFpQuuwrnye6PS7T1aM3XEPvFXiQbNu7.
Abuses to be avoided
It is not a unit of cryptocurrency (do not say: “I sent you 1 Tezos”)
It is not an entity (do not say: “Zomg Tezos is partnering with Gogolsoft” when some group of software developers that happens to work on Tezos convinced them to run some node on SkyNimbus™)
A unit of the cryptocurrency native to a Tezos chain (as in: “I sent you 2 tez”). Tez is invariable. It is not capitalized (except at the beginning of a sentence or when you would otherwise capitalize a noun). “I sent you 2 tez” and not “2 Tez”.
“Tezzies” seemed like a good idea for a very short period of time, a choice that immediately came to be regretted. Again, please keep “tez” invariable.
“XTZ” is an ISO-4217-compatible code for representing tez on the most economically relevant Tezos chain. Unless you have a very specific reason to use an ISO code for it, the term tez should be preferred. Situations where the ISO code might be useful typically involve accounting systems, exchange rates with other currencies, and anything that might need some sort of standardized code. Generally speaking, as of the day of this post, “XTZ” is vastly overused in situations where “tez” or even “Tezos” would be appropriate.